Vector control system for induction motor

ABSTRACT

A vector control system of an induction motor using the slip frequency control method comprises means for minimizing an error with regard to compensation for variation of a secondary resistance.

BACKGROUND OF THE INVENTION

The present invention relates generally to an adjustable speed drive system for an induction motor and more particularly, to a vector control system having compensation for a secondary resistance variation.

In the vector control system using the slip frequency control method, a secondary resistance of the induction motor is used for calculating a slip frequency, so that a variation in temperature of the secondary resistance causes a deterioration of torque control characteristic.

Some compensation methods of a variation of the secondary resistance are proposed. One is such that compensation for a secondary resistance variation is carried out by determining constants of the induction motor, and considering a difference between an output voltage of a model of the induction motor using these constants and an actual output voltage to be a variation due to a variation in temperature of the secondary constants.

With this method, however, in connection with a primary voltage, a command value due to a dead time of an inverter or a voltage drop of main circuit elements is sometimes different from an actual value, so that there is a limit with respect to achievement of high torque control accuracy. Moreover, this method cannot correspond to a change in temperature of a primary resistance.

Another method is such that compensation for a secondary resistance variation is carried out based on the fact that on the γ-δ axes having a primary current set as a reference axis, a voltage component of the δ axis which is normal to the primary current is not influenced by the primary resistance.

This method enables compensation for a secondary resistance variation which is robust to a change of the primary resistance, since a current control system is constructed on the d-q axes having a secondary magnetic flux set as a reference axis, and a component of a primary voltage variation on the δ axis is detected by a pulse width modulation (PWM) signal. For further information, see, for example, Paper D, vol. 112, No. 2, pp. 107-116, published in 1993 by Electric Society, or JP-A 3-253288.

With the latter method, however, due to a power source voltage, etc., the adjustable speed drive system has an upper limit of a possible output voltage, so that when a current control amplifier (refer hereinafter to as ACR amplifier) outputs a voltage command above the upper limit (which is generally called voltage saturation), an error is produced between a current command and a current passing through the induction motor. In view of this error, the latter method is available only in an area without voltage saturation. Further, when a voltage type PWM inverter is used in a voltage control part, a pulse lack is produced when the PWM pulse width becomes smaller than the dead time, resulting in a deterioration of current accuracy in the amplitude and phase. In this case, compensation for a secondary resistance variation has an error.

Moreover, although the latter method enables compensation for a secondary resistance variation which is robust to a change of the primary resistance, if set values of an exciting inductance M' (=M² /L₂ wherein L₂ is a secondary inductance) and an equivalent leakage inductance Lσ have an error, this method suffers an influence of a voltage error.

It is, therefore, an object of the present invention to provide a vector control system for an induction motor which enables more accurate compensation for a secondary resistance variation.

SUMMARY OF THE INVENTION

There is provided, according to the present invention, a vector control system for an induction motor which is driven by an inverter controlled by a pulse width modulation circuit, the system carrying out compensation for variation of a secondary resistance, comprising:

a first means for calculating target values I₁ d* and I₁ q* of d- and q-axis components of a primary current of the induction motor on d-q coordinates having a secondary magnetic flux set as a reference axis, said d-q coordinates being rotational coordinates which rotate in synchronism with a power source angular frequency of the induction motor;

a first coordinate transformation part arranged to calculate in accordance with said target values I₁ d* and I₁ q* of said d- and q-axis components a target value I₁ γ* (=I₁) of a γ-axis component of the primary current and a phase difference ψ on γ-δ coordinates having said phase difference ψ with respect to d-q axes and having said primary current I₁ set as a reference axis;

a slip angular frequency operation part arranged to input and calculate said ratio λ_(2d) */M* and said target value I₁ q* of said q-axis component so as to output a target value ω_(S) * of a slip angular frequency;

a second means for calculating target values V₁γ * and V₁ δ* of γ- and δ-axis components of a primary voltage in accordance with a ratio λ_(2d) */M* of a target value λ_(2d) * of said secondary magnetic flux to a target value M* of an exciting inductance, calculation results of said first coordinate transformation part and a command value ω₀ of said power source angular frequency;

a second coordinate transformation part arranged to transform a detection value of said primary current into actual γ- and δ-axis components I₁ γ and I₁ δ on said γ-δ coordinates;

a third means for calculating a variation ΔV₁ δ with respect to said V₁ δ* of said δ-axis component of said primary voltage in accordance with said target values I₁ δ* and I₁ δ* of said δ- and δ-axis components of said primary current and said actual γ- and δ-axis components I₁ γ and I₁ δ derived from said second coordinate transformation part;

a polar coordinate transformation part arranged to add said target values V₁ γ* and V₁ δ* derived from said second means to said variation ΔV₁ δ derived from said third means so as to output a magnitude |V₁ | of a vector of said primary voltage and a phase angle φ thereof with respect to a γ axis; and

a fourth means for minimizing an error with regard to compensation for variation of the secondary resistance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a first preferred embodiment of a vector control system for an induction motor according to the present invention;

FIG. 2 is a view similar to FIG. 1, showing a second preferred embodiment of the present invention;

FIG. 3 is a vector diagram showing a formula (5);

FIG. 4 is a view similar to FIG. 3, showing a formula (9);

FIG. 5 is a view similar to FIG. 4, upon load power running;

FIG. 6 is a view similar to FIG. 5, upon light-load power running;

FIG. 7 is a view similar to FIG. 6, showing E2 vector movement;

FIG. 8 is a view similar to FIG. 7, showing a δ-axis component of a voltage error;

FIG. 9 is a characteristic diagram of output voltage vs. weight function;

FIG. 10 is a view similar to FIG. 9, but of rotational speed of the induction motor vs. terminal voltage thereof;

FIG. 11 is a view similar to FIG. 10, but of rotational speed vs. weight function;

FIG. 12 is a view similar to FIG. 2, showing a third preferred embodiment of the present invention;

FIG. 13 is a T-I equivalent circuit of the induction motor;

FIG. 14A is a view similar to FIG. 8, upon power running;

FIG. 14B is a view similar to FIG. 14A, upon regeneration;

FIG. 15A is a view similar to FIG. 14A, upon power running; and

FIG. 15B is a view similar to FIG. 15A, upon regeneration.

DETAILED DESCRIPTION OF THE INVENTION

Referring to the drawings, preferred embodiments of a vector control system for an induction motor will be described.

Before entering the first embodiment, a detailed description will be made with regard to inconvenience encountered in JP-A 3-253288.

When using a T-I type equivalent circuit (for reference, see FIG. 13), and shown in the form of a vector space, a voltage-current equation of the induction motor is generally given by a formula (1): ##EQU1## wherein ₁ : primary voltage,

₁ : primary current,

R₁, R₂ ': primary and secondary resistances,

λ₂ : secondary magnetic flux,

M: exciting inductance,

ω: primary power source angular frequency,

ω_(S) : slip angular frequency,

Lσ: leakage inductance,

M': =M² /L₂,

P: =d/dt: differential operator.

Assuming that only steady terms are available in the formula (1), the formula (1) can be rewritten as a formula (2): ##EQU2##

In view of a steady state, when shown in a Feather vector, the formula (2) is replaced by a formula (3): ##EQU3##

When a current control is carried out, and thus a vector I₁ is constant, a vector λ₂ /M and a vector V₁ are obtained.

From the formula (3), second line, a formula (4) is obtained: ##EQU4## wherein α=ω_(S) (M'/R₂ ').

Additionally, from the formula (3), first line, and the formula (4), a formula (5) is obtained: ##EQU5##

FIG. 3 shows a vector diagram of the formula (5).

In JP-A 3-253288, conditions of compensation for a secondary resistance variation (refer hereinafter to as R₂ compensation) are as follows: ##EQU6## wherein a reference with asterisk designates a data or target value of the induction motor stored in a control system, whereas a reference without asterisk designates a constant or value of the actual induction motor. Here, an inconsistency is found only in the third condition (R₂ '* ≠R₂ '). From the above conditions and since vector I1*=I₁ d*+jI₁ q* (wherein I₁ d* and I₁ q* are target values of d-axis and q-axis components of I1), the slip angular frequency ω_(S) is expressed by a formula (7): ##EQU7##

When applying α=ω_(S) (M'/R₂ ') to the formula (7), a formula (8) is obtained: ##EQU8##

Here, α is varied with a ratio of R₂ '*/R₂ ', however, the term of α in the formula (5) is given by a formula (9): ##EQU9##

From the formula (9), it is understood that regardless of α, the amplitude is 1, and only the orthogonal ratio is changed. The formula (9) is diagrammatically shown by FIG. 4. Thus, in connection with a variation of the vector V₁, when α is varied by R₂ ', only a third term in the formula (5) is changed. This third term is given by a formula (10): ##EQU10##

Therefore, the locus of a secondary voltage E₂ is as shown in FIG. 5 upon load power running, and as shown in FIG. 6 upon light-load power running. In case that R₂ compensation is carried out based on a voltage error, when extracting the voltage error in the direction of a tangent line of the semicircular E₂ locus which varies ideally from α=0 to α=∞ in FIGS. 5 and 6, components of the voltage error are symmetrical whether R₂ ' deviates to the positive or the negative. However, in reality, the resistance R₁ is also varied with the temperature. Thus, in connection with the voltage error components, it is preferable to use a δ-axis component which is normal to a component of (R₁ ·I₁) to extract an angular component which contacts the E₂ locus as shown in FIG. 7. This will easily be understood in FIG. 8. The above uses a component which is normal to a term of R₁ in the formula (5). This component is given by the formula (11): ##EQU11##

The above method is a fundamental principle for R₂ compensation shown in JP-A 3-253288. In this method, since the width of the PWM pulse is reduced as voltage approaches a saturation, a pulse lack is produced due to a switching lag and dead time of an inverter, and an operation of dead time compensation. As a result, a current detection error causes an error in the current control accuracy. Further, in the above method, a current control should be carried out normally so that a current command corresponds to an actual current. Thus, a current error causes a malfunction of R₂ compensation.

Next, a consideration will be made with regard to an influence of the current error on R₂ compensation. When expressing the current error by an amplitude component and a phase component, a formula (12) is obtained: ##EQU12##

When applying the formula (12) to the formula (5), the voltage error component due to the current error is expressed by a formula (13): ##EQU13##

If only a j component is extracted in the formula (13), a voltage error component on the δ axis due to the current error is expressed by a formula (14): ##EQU14##

Here, at no load (α=0), an influence of ΔI₁ γ is only a factor of malfunction of R₂ compensation, whereas at load (α=0 to 5), an influence of ΔI₁ δ is increased. Measurement of the current error upon real occurrence of a pulse lack reveals that the error of ΔI₁ δ is greater than that of ΔI₁ γ due to a pulse lack, and an amount thereof is substantially constant regardless of a current load, and presence of a pulse lack determines whether the current error is produced or not. Thus, when using the voltage error on the δ axis, no error is produced at no load, whereas a greater error is produced at load.

If the secondary resistance is incorrectly modificated by the above error component, ω_(S) in α=ω_(S) (M'/R₂ ') is different from the vector control condition, so that a value of α has an error, and semicircular E₂ vector movement is produced as shown in FIG. 7. Referring to FIG. 7, if α is modified to a small value, a radius of E₂ becomes greater, and a voltage saturation is advanced further, resulting in a further lowering of α. As a result, if the current error is produced due to a pulse lack, and once α is modified in the lowered direction, a voltage is increased up to a limit of saturation by a positive feedback operation, a value of α becomes smaller, and cannot return from that state. Thus, R₂ compensation using the δ axis is not available in a pulse lacked area wherein the current and voltage accuracy is deteriorated.

In the vicinity of a voltage saturation, it is reasonable to use a voltage component other than the voltage error on the δ axis. In case of the current control system having a greater phase error of the current accuracy, only the amplitude of the vector is used in view of a large error of a phase component. Moreover, referring to FIG. 7, it is understood that if α is changed by a variation of R₂, the voltage amplitude is also changed at load, so that R₂ compensation is possible based on an error component of the voltage amplitude. However, at no load, the voltage amplitude error is not influenced by an R₂ variation in the same manner as the voltage error on the δ axis, so that an interruption of R₂ compensation is needed.

Referring to FIGS. 1 and 3-11, there is shown a first preferred embodiment of the present invention.

Referring to FIG. 1, A₁ designates a secondary magnetic flux command amplifier which outputs λ₂ */M* in response to a rotor angular frequency ω_(r) out of a speed detection part C₃. It is to be noted that a reference with asterisk designates a target value. The command amplifier 11 outputs λ_(2do) */M until ω_(r) exceeds a predetermined value. When ω₄ exceeds the predetermined value, and enters a field control area, λ_(2d) */M, becomes smaller in accordance with ω₄.

A₂ designates an operation part which carries out an operation of λ₂ */M* {1+(L₂ */R₂ '*) P}.

B₁ designates a first coordinate transformation part which serves to operate, in accordance with target values I₁ d*, I₁ q, of d- and q-axis components of the primary current I₁ of the induction motor IM, a phase difference ψ between a target value I₁ γ, and the d and γ axes in the γ-δ coordinates having a primary current I₁ set as a reference axis.

B₂ designates an ideal voltage operation part which operates a target value of the primary voltage V₁. The operation part B₂ inputs sin ψ, I₁, cos ψ derived from the first coordinate transformation part B₁, and λ₂ */M* derived from the secondary magnetic flux command amplifier 11, and the power source angular frequency, and operates these so as to obtain target values V₁ γ*, V₁ δ*.

6 designates a second coordinate transformation part which detects the primary current I₁ of the induction motor IM, and transforms detection values I_(U), I_(W) into γ- and δ-axis components I₁ γ, I₁ δ in the γ-δ coordinates. The components I₁ γ, I₁ δ are compared with target values I₁ γ*, I₁ δ* (=0), respectively, and deviations thereof are input to proportional-integral (PI) amplifiers 7, 8 which serve as an ACR amplifier.

The PI amplifiers 7, 8 output error variations ΔV₁ γ, ΔV₁ δ, respectively, which are added to target values ΔV₁ γ*, ΔV₁ δ* derived from the ideal voltage operation part B₂, and input to a polar coordinate transformation part 9. In accordance with input values, the polar coordinate transformation part 9 outputs a magnitude |V₁ | of the vector V₁ of the primary voltage, and a phase angle φ thereof with the γ axis. The phase angle φ is added to the phase difference ψ and θ (ω₀ t) as will be described later, which is input to a PWM circuit C₁ together with the magnitude |V₁ |, and transformed into a primary voltage command value corresponding to the U, V, and W phase, thus controlling a voltage of an inverter C₂.

11 designates a slip angular frequency operation part which receives λ_(2d) */M* and I₁ q* so as to obtain a slip angular frequency ω_(S) on the output side thereof.

12 designates an identification circuit part which serves at no load to input ΔV₁ γ and I₁ d* so as to calculate a variation of the primary resistance for identification of R₁, and also to receive ΔV₁ d, ω, and λ_(2d) */M* So as to calculate a variation of the exciting inductance M for identification of M' (=M² /L₂).

Here, a determination whether a no-load running is effective or not and a drive timing of the identification circuit part 12 are carried by an output of a comparator 13. In case that a rated torque current is 100%, and a value of 5% thereof is a set value, for example, if a comparison reveals that the set value is smaller than I₁ q*, the comparator 13 determines that a no-load running is effective, and drives the identification circuit part 12.

14 designates a PI amplifier which serves as a voltage variation part control amplifier, and receives on the input side thereof an error voltage ΔV used for R₂ compensation as will be described later. On the output side of the PI amplifier 14, a first adder (no numeral) adds a variation Δω_(S) of the slip angular frequency to the target value ω_(S) * of the slip angular frequency through a switching part 16 so as to obtain a new target value ω_(S) * thereof at the output side of the adder. In a second adder (no numeral), this new target value ω_(S) * is added to the rotor angular frequency ω_(r) so as to obtain a primary angular frequency ω₀ as an added output. The primary angular frequency ω₀ is provided to the ideal voltage operation part 5₂, and also to an integrator 15 so as to obtain θ.

17 designates a first operation part which receives the outputs V1γ*, V₁ δ* of the ideal voltage operation part B₂ for polar coordinate transformation. As an output of the first operation part 17, an amplitude component |V₁ *| of the primary voltage is obtained. A second operation part 18 receives the amplitude component |V₁ *| at the positive terminal thereof, and the output |V₁ | of the polar coordinate transformation part 9 at the negative terminal thereof. As an output of the second operation part 18, an error Δ|V₁ | of the two (i.e., error component of the voltage amplitude) is obtained. This output Δ|V₁ | is provided to a third operation part 19 having a weight function to a rotating speed.

20 designates a fourth operation part which having a weight function to a rotating speed. The fourth operation part 20 receives on the input side thereof a deviation with respect to the δ-axis error components ΔV₁ δ, ΔV₁ δ* (=0) derived from the PI amplifier 8. Outputs of the third and fourth operation parts 19, 20 are added in an adder 21 which provides an added output ΔV (i.e., error voltage used for R₂ compensation) to be provided to the PI amplifier 14.

The reason of giving to the third and fourth operation parts 19, 20 the weight function to the rotational speed is as follows: Ordinarily, referring to FIGS. 9-11, when simply changed over by a switch, both output voltages (i.e., amplitude and δ-axis components) of the third and fourth operation parts 19, 20 are changed discontinuously. Thus, for smooth switching, it is preferable to use the weight function K. When giving the weight function K to the third and fourth operation parts 19, 20, the error voltage ΔV used for R₂ compensation is given by a formula (15):

    ΔV=KVδ×(ΔV.sub.1 δ)+K.sub.VR× (Δ|V.sub.1 |)                     (15)

FIG. 9 graphically shows the relationship given by the formula (15). In a characteristic diagram of the weight function K shown in FIG. 9, the output voltage V is taken on the x axis, which has a large change, however, since it also varies with the load. On the other hand, as seen in FIG. 10, the terminal voltage of the induction motor IM is increased substantially in proportion to the rotational speed thereof. By using this, the rotational speed can be taken on the x axis as shown in FIG. 11. In the first embodiment as shown in FIG. 1, the third and fourth operation parts 19, 20 have the weight function defined in such a manner, respectively.

Referring to FIG. 2, there is sown a second preferred embodiment of the present invention. A voltage detector 22 is arranged for detecting an output voltage of the inverter C₂. A voltage detected by the detector 22 is provided to the negative terminal of the second operation part 18. According to this embodiment, voltage accuracy of the PWM circuit C₁ fails to be concerned in control accuracy, resulting in improvent thereof.

Referring to FIGS. 12-15B, there is shown a third preferred embodiment of the present invention.

When expressed by two-axes on the rotational coordinates, and using a T-I type equivalent circuit as shown in FIG. 13, an equation of the induction motor is generally given by a formula (1'): ##EQU15## wherein V₁ d, V₁ q: d- and q-axis components of a primary voltage,

I₁ d, I₁ q: d- and q-axis components of a primary current,

R₁, R₂ : primary and secondary coil resistances,

L₁, L₂ : primary and secondary inductances,

M: primary and secondary mutual inductances,

ω₁ : primary angular frequency,

ω_(S) : slip angular frequency,

Lσ: L1-M² /L₂,

R₂ ': (M/L₂)² ·R₂,

λ₂ d/M: I₁ d+(L₂ /M)I₂ d,

λ₂ q/M: I₁ q+(L₂ /M)I₂ q.

Here, a vector control condition is given by a formula (2'): ##EQU16## wherein T is a torque, and POLE is the number of poles of the induction motor.

By establishment of the formula (2'), a formula (3') is established, obtaining the torque current I₁ q and torque T linearized.

    λ.sub.2 q/M=0

    I.sub.1 d=λ.sub.2 d/M                               (3')

At that moment, a voltage-current vector diagram is as shown in FIGS. 14A and 14B. FIG. 14A is a vector diagram upon power running, whereas FIG. 14B is a vector diagram upon regeneration.

In the formula (1'), a consideration will be made with regard to a case that due to occurrence of a variation of the secondary resistance, a value thereof R₂ ' is changed to R₂ 'x. When carrying out the vector control on condition that the other constants R₁, Lσ, M' correspond to those of the model of the induction motor, and errors of the frequency, voltage and current are neglected, I₁ d, I₁ q and ω_(S) are fixed if the ACR amplifier operates in response to a command value, whereas λ₂ d/M, λ₂ q/M, V₁ d, V₁ q are varied due to a variation of the secondary resistance R₂ '.

This variation appears in the formula (1'), lines 3 and 4, and is given by a formula (4'): ##EQU17##

When applying ω_(S) of the formula (2') to the formula (4'), and having a change of λ₂ d and λ₂ q to λ₂ dx and λ₂₂ qx, respectively, a solution of the simultaneous equations of the formula (4') is given by a formula (5'): ##EQU18##

From the relationship of (x² -ax)=(x-a/2)² -(a/2)², the formula (5') is developed to a formula (6'): ##EQU19##

The formula (6') is diagrammatically shown by a circle having a center of (I₁ d/2, I₁ q/2), and a radius of {(I₁ d/2)² +(I₁ q/2)² }^(1/2).

Therefore, when the secondary resistance R₂ ' is varied in the steady state, the voltage-current vector diagram is as shown in FIGS. 15A and 15B. FIG. 15A is a vector diagram upon power running, whereas FIG. 15B is a vector diagram upon regeneration. As shown in FIGS. 15A and 15B, the secondary magnetic flux λ₂ /M is changed in the direction of a tangent line Pd of a first circle having a center O, whereas the secondary voltage E₂ is changed in the direction of a tangent line Pq of a second circle having a center O'.

As seen from FIGS. 15A and 15B, in connection with the secondary voltage E₂ * of the model, the actual secondary voltage E₂ is given by a formula (7'):

    E.sub.2 =V.sub.1 -(R.sub.1 I.sub.1 +jωLσI.sub.1)(7')

When obtaining an error voltage between E₂ * and E₂, and transforming the coordinates of the error voltage in the reverse direction of a phase ψ between the γ axis of the primary current I₁ and the d axis of the secondary magnetic flux, i.e., into the - ψ coordinates, the error voltage is in the direction of the tangent line of the second circle, thus obtaining the coordinates which enables an effective detection of a voltage variation due to the secondary resistance R₂ '.

The above is summarized as follows:

1) The q-axis component of the secondary voltage E₂ * of the model is obtained:

    E.sub.2 q*=ω.sub.1 M'(λ.sub.2 d/M)*

2) The d- and q-axis components of the actual secondary voltage E₂ are obtained from the output voltage of the induction motor:

    E.sub.2 d=V.sub.1 d-(R.sub.1 I.sub.1 d-ωLσI.sub.1 q)

    E.sub.2 q=V.sub.1 q-(R.sub.1 I.sub.1 q+ωLσI.sub.1 d)

3) The error voltage between E₂ * and E₂ is obtained:

    ΔE.sub.2 d=E.sub.2 d-0

    ΔE.sub.2 q=E.sub.2 q-E.sub.2 q*

4) The phase ψ of the primary current is obtained:

    ψ=tan.sup.-1 (I.sub.1 q*/I.sub.1 d*)

5) The coordinates of the error voltage components ΔE₂ d, ΔE₂ q are transformed into the - ψ coordinates:

    ΔE.sub.R2H =sign(I.sub.1 q*)·(ΔE.sub.2 d·cos ψ-ΔE.sub.2 q·sin ψ)

The secondary resistance R₂ * of the model is corrected by ΔE_(R2H). That is, if ΔE_(R2H) is positive, R₂ * is reduced, whereas if ΔE_(R2H) is negative, R₂ * is increased.

Referring to FIG. 12, in a vector control part 101, out of a current command I₁ d* (=-λ₂ d/M) of the d axis and a current command I₁ q* of the q axis, and detected current components I₁ d, I₁ q of the primary current, ACR amplifiers 101A, 101B fetch d- and q-axis voltage commands V₁ d*, V₁ q*, respectively. A PWM circuit 101C provides three-phase output voltages Vu, Vv, Vw which serves as a primary voltage of the induction motor 101D.

A slip frequency operation part 101E calculates a slip frequency ω_(S) from the current commands I₁ d*, I₁ q* and a constant R₂ '/M', which is added to a an angular frequency ω_(r) detected by a speed detector 101F of a rotor of the induction motor 101D so as to obtain a primary angular frequency ω₁ 1. The primary angular frequency ω₁ 1 is integrated by an integrator 101G to obtain a phase angle by which the PWM circuit 101C has PWM signals of the three-phase voltages Vu, Vv, Vw. A current conversion part 101H converts three-phase currents Iu, Iv, Iw into the above current components I₁ d, I₁ q.

A secondary resistance compensation part having elements 102-109 corrects the secondary resistance R₂ ' of the slip frequency operation part 101E.

The secondary induced voltage detection part 102 subtracts voltage drops I₁ dR₁ and I₁ qω₁ 1Lσ of the primary resistance R₁ and the primary equivalent leakage inductance Lσ due to the primary current components from the voltage command outputs V₁ d*, V₁ q* of the ACR amplifiers 101A, 101B, respectively, thus detecting a secondary induced voltage.

The secondary reverse voltage operation part 103 calculates out of the current command I₁ d* and a preset constant ωM' a secondary reverse voltage when having the ideal vector control.

The phase operation part 104 calculates out of the current commands I₁ d*, I₁ q* a phase ψ of a vector of the primary current with respect to the d axis:

    ψ=tan.sup.-1 (I.sub.1 q*/I.sub.1 d*)

The error voltage detection part 105 subtracts a voltage of the secondary reverse voltage operation part 103 from the detected voltage of the secondary induced voltage detection part 102. This subtraction result is multiplied by sine and cosine waves with the phase ψ of the phase operation part 104 so as to calculate coordinate components of a negative phase of the phase ψ, thus obtaining an error voltage.

The correction operation part 106 corrects the polarity of the error voltage by multiplying a detection value thereof by +1 or -1 in accordance with a sign of the q-axis current command I₁ q*.

The correction selection circuit 107 carries out an interruption of correction of the secondary resistance R₂ ' based on error voltage detection when a slip angle is smaller than the phase ψ calculated by the phase operation part 104.

The secondary resistance correction part 108 having an integral characteristic estimates the secondary resistance R₂ ' in a predetermined ratio when the correction selection circuit 107 selects the error voltage, and corrects thereby a set value of the secondary resistance R₂ ' of the slip frequency operation part 101E.

The primary resistance estimation part 109 estimates the primary resistance R₁ set in the secondary induced voltage detection part 102 out of a temperature sensor 109A embedded in the primary winding of the induction motor 101D, thus correcting a set value of the primary resistance R₁.

Having described the present invention in connection with the preferred embodiments, it is to be noted that the present invention is not limited thereto, and various changes and modifications are possible without departing from the spirit of the present invention. 

What is claimed is:
 1. A vector control system for an induction motor which is driven by an inverter controlled by a pulse width modulation circuit, the system carrying out compensation for variation of a secondary resistance, comprising:first means for calculating target values I₁ d* and I₁ q* of d- and q-axis components of a primary current of the induction motor on d-q coordinates having a secondary magnetic flux set as a reference axis, said d-q coordinates being rotational coordinates which rotate in synchronism with a power source angular frequency of the induction motor; a first coordinate transformation part arranged to calculate in accordance with said target values I₁ d* and I₁ q* of said d- and q-axis components a target value I₁ γ* (=I₁) of a γ-axis component of the primary current and a phase difference ψ on γ-δ coordinates having said phase difference ψ with respect to d-q axes and having said primary current I₁ set as a reference axis; a slip angular frequency operation part arranged to input and calculate a ratio λ_(2d) */M* and said target value I₁ q* of said q-axis component so as to output a target value ω_(S) * of a slip angular frequency; second means for calculating target values V₁ γ* and V₁ δ* of γ- and δ-axis components of a primary voltage in accordance with a ratio λ_(2d) */M* of a target value λ_(2d) * of said secondary magnetic flux to a target value M* of an exciting inductance, calculation results of said first coordinate transformation part and a command value ω₀ of said power source angular frequency; a second coordinate transformation part arranged to transform a detection value of said primary current into actual γ- and δ-axis components I₁ γ and I₁ δ on said γ-δ coordinates; third means for calculating a variation ΔV₁ δ with respect to said V₁ δ* of said δ-axis component of said primary voltage in accordance with said target values I₁ γ* and I₁ δ* of said γ- and δ-axis components of said primary current and said actual γ- and δ-axis components I₁ γ and I₁ δ derived from said second coordinate transformation part; a polar coordinate transformation part arranged to add said target values V₁ γ* and V₁ δ* derived from said second means to said variation ΔV₁ δ derived from said third means so as to output a magnitude |V₁ | of a vector of said primary voltage and a phase angle φ thereof with respect to a γ axis; and fourth means for minimizing an error with regard to compensation for variation of the secondary resistance, and including a first operation part arranged to carry out a polar coordinate transformation of said target values V₁ γ* and V₁ δ* of said second means so as to output an amplitude component |V₁ *|; a second operation part arranged to calculate a deviation between said amplitude component |V₁ *| of said first operation part and said magnitude |V₁ | of said vector of said primary voltage so as to output an amplitude variation error Δ|V₁ |; third and fourth operation parts arranged to input said amplitude variation error Δ|V₁ | derived from said second operation part and said variation ΔV₁ δ derived from said third means and provide outputs by switching the two; and a third adder arranged to add said outputs of said third and fourth operation parts so as to input said voltage variation control part.
 2. A vector control system as claimed in claim 1, further comprising:a voltage detector arranged on the output side of the inverter to detect an inverter voltage, said inverter voltage being provided to said second operation part so as to calculate a deviation between an output of said voltage detector and an output of said first operation part.
 3. A vector control system as claimed in claim 1, wherein said fourth means further comprises:a secondary induced voltage detection part arranged to obtain a detection voltage by subtracting a voltage drop in a primary resistance R₁ and a primary equivalent leakage inductance Lσ due to a primary current component from an output voltage of current control amplifiers of d and q axes; a secondary reverse voltage operation part arranged to calculate in accordance with a preset constant of the induction motor and a current command value a secondary reverse voltage when having an ideal vector control; a phase operation part arranged to calculate a phase ψ of a vector of said primary current with respect to said d axis in accordance with said current command value; an error voltage detection part arranged to subtract said secondary reverse voltage of said secondary reverse voltage operation part from said detection voltage of said secondary induced voltage detection part so as to obtain an error voltage, said error voltage serving to calculate a coordinate component of a reverse phase of said phase ψ; a correction operation part arranged to change a polarity of said error voltage of said error voltage detection part in accordance with a sign of a current command of a q axis; and a secondary resistance correction part arranged downstream of said correction operation part to estimate the secondary resistance by said error voltage so as to correct the secondary resistance for calculation of said slip angular frequency.
 4. A vector control system as claimed in claim 1, wherein said third and fourth operation parts have a weight function to a rotating speed of the induction motor, respectively.
 5. A vector control system for an induction motor which is driven by an inverter controlled by a pulse width modulation circuit, the system carrying out compensation for variation of a secondary resistance, comprising:first means for calculating target values I₁ d* and I₁ q* of d- and q-axis components of a primary current of the induction motor on d-q coordinates having a secondary magnetic flux set as a reference axis, said d-q coordinates being rotational coordinates which rotate in synchronism with a power source angular frequency of the induction motor; a first coordinate transformation part arranged to calculate in accordance with said target values I₁ d* and I₁ q* of said d- and q-axis components a target value I₁ γ* (=I₁) of a γ-axis component of the primary current and a phase difference ψ on γ-δ coordinates having said phase difference ψ with respect to d-q axes and having said primary current I₁ set as a reference axis; second means for calculating target values V₁ γ* and V₁ δ* of γ- and δ-axis components of a primary voltage in accordance with a ratio λ_(2d) */M* of a target value λ_(2d) * of said secondary magnetic flux to a target value M* of an exciting inductance, calculation results of said first coordinate transformation part and a command value ω₀ of said power source angular frequency; a slip angular frequency operation part arranged to input and calculate said ratio λ_(2d) */M* and said target value I₁ q* of said q-axis component so as to output a target value ω_(S) * of a slip angular frequency; a second coordinate transformation part arranged to transform a detection value of said primary current into actual γ- and δ-axis components I₁ γ and I₁ δ on said γ-δ coordinates; third means for calculating a variation ΔV₁ δ with respect to said V₁ δ* of said δ-axis component of said primary voltage in accordance with said target values I₁ γ* and I₁ δ* of said γ- and δ-axis components of said primary current and said actual γ- and δ-axis components I₁ γ and I₁ δ derived from said second coordinate transformation part; a polar coordinate transformation part arranged to add said target values V₁ γ* and V₁ δ* derived from said second means to said variation ΔV₁ δ derived from said third means so as to output a magnitude |V₁ | of a vector of said primary voltage and a phase angle φ thereof with respect to a γ axis; and fourth means for minimizing an error with regard to compensation for variation of the secondary resistance, the fourth means includinga secondary induced voltage detection part arranged to obtain a detection voltage by subtracting a voltage drop in a primary resistance R₁ and a primary equivalent leakage inductance Lσ due to a primary current component from an output voltage of current control amplifiers of d and q axes; a secondary reverse voltage operation part arranged to calculate in accordance with a preset constant of the induction motor and a current command value a secondary reverse voltage when having an ideal vector control; a phase operation part arranged to calculate a phase ψ of a vector of said primary current with respect to said d-axis in accordance with said current command value; an error voltage detection part arranged to subtract said secondary reverse voltage of said secondary reverse voltage operation part from said detection voltage of said secondary induced voltage detection part so as to obtain an error voltage, said error voltage serving to calculate a coordinate component of a reverse phase of said phase ψ; a correction operation part arranged to change a polarity of said error voltage of said error voltage detection part in accordance with a sign of a current command of said q-axis; and a secondary resistance correction part arranged downstream of said correction operation part to estimate the secondary resistance by said error voltage so as to correct the secondary resistance for calculation of said slip angular frequency. 